Wavefront sensing in space for localizing sound has been in practice since the pioneering work by Blumlein (as described in British Patent 394325 to Blumlein, “Improvements in and Relating to Sound-Transmission, Sound-Recording and Sound-Reproducing Systems”, 1933), a precursor to the advances in binaural signal processing that we know today. The direction of a traveling wave can be inferred directly by sensing spatial differentials on a sub-wavelength scale, a principle exploited in biology, e.g., by the Sarcophagid Parasitoid Fly Emblemasoma sp. (Robert, D., R. N. Miles and R. R. Hoy, “Tympanal Hearing in the Sarcophagid Parasitoid Fly Emblemasoma sp.: the Biomechanics of Directional Hearing”, 1999). Differentials of a sound pressure field measured in different directions can be linearly combined to implement steerable spatial filters for acoustic beamforming (U.S. Pat. No. 6,041,127 to Elko). Differential sensing for directional sensing is also the guiding principle in monopulse radar and sonar (e.g., U.S. Pat. No. 6,356,231 to Zheng, et al.).
Super-resolution spectral methods are commonly used to localize multiple narrowband sources (Haykin, S. Adaptive Filter Theory, 2nd. Ed., Prentice Hall, 1991). Yet little is known about the problem of localizing and separating multiple broadband sources. Separating mixtures of delayed sources has been addressed with Independent Component Analysis (ICA, e.g., U.S. Pat. No. 5,383,164 to Sejnowski, et al., U.S. Pat. No. 5,706,402 to Bell, U.S. Pat. No. 6,185,309 to Attias, and U.S. Pat. No. 6,424,960 to Lee, et al.), but requires a large number of parameters to obtain sufficient temporal resolution for precise localization. Adapting delays (U.S. Pat. No. 5,675,659 to Torkkola and U.S. Pat. No. 5,694,474 to Ngo, et al.) reduces the number of parameters, but is prone to local optima.
The approach we present here avoids the problem of separating delayed mixtures by observing spatial differentials of the field, which convey an instantaneous linear mixture of the time-differentiated sources. The resulting formulation is equivalent to that of standard (instantaneous linear) ICA, and a number of approaches exist for such blind separation, e.g. as demonstrated in U.S. Pat. No. 5,315,532 to Comon and U.S. Pat. No. 5,706,402 to Bell, and some leading to efficient VLSI implementation (e.g., Cohen, M. H. and A. G. Andreou, “Current-Mode Subthreshold MOS Implementation of Herault-Jutten Autoadaptive Network,” IEEE J. Solid-State Circuits, vol. 27, pp. 714-727, May 1992). The mixing coefficients obtained from ICA yield the angles of the incoming waves. Therefore the method claimed here can be seen as a combination of differential wave sensing and ICA, performing at once blind separation and localization of traveling waves.
Spatial differentials can be either obtained using gradient sensors (e.g., differential microphones as customarily used in hearing aids, as shown in U.S. Pat. No. 5,033,090 to Weinrich), or from discrete observations on a grid using a sensor array. The presented technique makes it possible to separate multiple signals with miniature distributed sensors or sensor arrays that are integrated on a single MEMS or VLSI chip.